The Inductive Significance of Observationally Indistinguishable Spacetimes

Results on the observational indistinguishability of spacetimes demonstrate the impossibility of determining by deductive inference which is our spacetime, no matter how extensive a portion of the spacetime is observed. These results do not illustrate an underdetermination of theory by evidence, since they make no decision between competing theories and they make little contact with the inductive considerations that must ground such a decision. Rather, these results express a variety of indeterminism in which a specification of the observable past always fails to fix the remainder of a spacetime. This form of indeterminism is more troubling than the familiar indeterminism of quantum theory. The inductive inferences that can discriminate among the different spacetime extensions of the observed past are here called “opaque,” which means that we cannot readily see the warrant that lies behind them.